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<!-- ==================== MODULE DESCRIPTION ==================== -->
<h1 class="epydoc">Module norms</h1><p class="nomargin-top"><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html">source&nbsp;code</a></span></p>
<p>This package implements operations of fuzzy logic.</p>
<p>Basic operations are <tt class="rst-docutils literal">and (&amp;)</tt>, <tt class="rst-docutils literal">or (|)</tt> and <tt class="rst-docutils literal">not (~)</tt>. Those are
implemented as functions of, respectively, two, two and one values. The <tt class="rst-docutils literal">and</tt>
is the t-norm of the fuzzy logic, and it is a function that takes two values and
returns the result of the <tt class="rst-docutils literal">and</tt> operation. The <tt class="rst-docutils literal">or</tt> is a function that takes
two values and returns the result of the <tt class="rst-docutils literal">or</tt> operation. the <tt class="rst-docutils literal">not</tt> is a
function that takes one value and returns the result of the <tt class="rst-docutils literal">not</tt> operation.
To implement your own operations there is no need to subclass -- just create the
functions and use them where appropriate.</p>
<p>Also, implication and aglutination functions are defined here. Implication is
the result of the generalized modus ponens used in fuzzy inference systems.
Aglutination is the generalization from two different conclusions used in fuzzy
inference systems. Both are implemented as functions that take two values and
return the result of the operation. As above, to implement your own operations,
there is no need to subclass -- just create the functions and use them where
appropriate.</p>
<p>The functions here are provided as convenience.</p>

<!-- ==================== FUNCTIONS ==================== -->
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ZadehAnd" class="summary-sig-name">ZadehAnd</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      And operation as defined by Lofti Zadeh.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehAnd">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ZadehOr" class="summary-sig-name">ZadehOr</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Or operation as defined by Lofti Zadeh.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehOr">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ZadehNot" class="summary-sig-name">ZadehNot</a>(<span class="summary-sig-arg">x</span>)</span><br />
      Not operation as defined by Lofti Zadeh.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehNot">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ZadehImplication" class="summary-sig-name">ZadehImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication operation as defined by Zadeh.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehImplication">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#DrasticProduct" class="summary-sig-name">DrasticProduct</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Drastic product that can be used as and operation</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DrasticProduct">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#DrasticSum" class="summary-sig-name">DrasticSum</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Drastic sum that can be used as or operation</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DrasticSum">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#EinsteinProduct" class="summary-sig-name">EinsteinProduct</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Einstein product that can be used as and operation.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#EinsteinProduct">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#EinsteinSum" class="summary-sig-name">EinsteinSum</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Einstein sum that can be used as or operation.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#EinsteinSum">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#MamdaniImplication" class="summary-sig-name">MamdaniImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication operation as defined by Mamdani.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#MamdaniImplication">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#MamdaniAglutination" class="summary-sig-name">MamdaniAglutination</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Aglutination as defined by Mamdani.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#MamdaniAglutination">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ProbabilisticAnd" class="summary-sig-name">ProbabilisticAnd</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      And operation as a probabilistic operation.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticAnd">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ProbabilisticOr" class="summary-sig-name">ProbabilisticOr</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Or operation as a probabilistic operation.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticOr">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ProbabilisticNot" class="summary-sig-name">ProbabilisticNot</a>(<span class="summary-sig-arg">x</span>)</span><br />
      Not operation as a probabilistic operation.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticNot">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ProbabilisticImplication" class="summary-sig-name">ProbabilisticImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication as a probabilistic operation.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticImplication">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#ProbabilisticAglutination" class="summary-sig-name">ProbabilisticAglutination</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication as a probabilistic operation.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticAglutination">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#DienesRescherImplication" class="summary-sig-name">DienesRescherImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Natural implication as in truth table, defined by Dienes-Rescher</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DienesRescherImplication">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#LukasiewiczImplication" class="summary-sig-name">LukasiewiczImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication of the Lukasiewicz three-valued logic.</td>
          <td align="right" valign="top">
            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#LukasiewiczImplication">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a href="peach.fuzzy.norms-module.html#GodelImplication" class="summary-sig-name">GodelImplication</a>(<span class="summary-sig-arg">x</span>,
        <span class="summary-sig-arg">y</span>)</span><br />
      Implication as defined by Godel.</td>
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            <span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#GodelImplication">source&nbsp;code</a></span>
            
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<!-- ==================== VARIABLES ==================== -->
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        <a href="peach.fuzzy.norms-module.html#__doc__" class="summary-name">__doc__</a> = <code title="&quot;&quot;&quot;
This package implements operations of fuzzy logic.

Basic operations are ``and (&amp;)``, ``or (|)`` and ``not (~)``. Those ar\
e
implemented as functions of, respectively, two, two and one values. Th\
e ``and``
is the t-norm of the fuzzy logic, and it is a function that takes two \
..."><code class="variable-ellipsis">...</code></code>
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    </td><td class="summary">
        <a name="ZADEH_NORMS"></a><span class="summary-name">ZADEH_NORMS</span> = <code title="ZadehAnd, ZadehOr, ZadehNot">ZadehAnd, ZadehOr, ZadehNot</code><br />
      Tuple containing, in order, Zadeh and, or and not operations
    </td>
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="DRASTIC_NORMS"></a><span class="summary-name">DRASTIC_NORMS</span> = <code title="DrasticProduct, DrasticSum, ZadehNot">DrasticProduct, DrasticSum, ZadehNot</code><br />
      Tuple containing, in order, Drastic product (and), Drastic sum (or) and Zadeh
not operations
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="EINSTEIN_NORMS"></a><span class="summary-name">EINSTEIN_NORMS</span> = <code title="EinsteinProduct, EinsteinSum, ZadehNot">EinsteinProduct, EinsteinSum, ZadehNot</code><br />
      Tuple containing, in order, Einstein product (and), Einstein sum (or) and
Zadeh not operations
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a name="MAMDANI_INFERENCE"></a><span class="summary-name">MAMDANI_INFERENCE</span> = <code title="MamdaniImplication, MamdaniAglutination">MamdaniImplication, MamdaniAglutination</code><br />
      Tuple containing, in order, Mamdani implication and algutination
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    </td><td class="summary">
        <a name="PROB_NORMS"></a><span class="summary-name">PROB_NORMS</span> = <code title="ProbabilisticAnd, ProbabilisticOr, ProbabilisticNot">ProbabilisticAnd, ProbabilisticOr, ProbabilisticNot</code><br />
      Tuple containing, in order, probabilistic and, or and not operations
    </td>
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      <span class="summary-type">&nbsp;</span>
    </td><td class="summary">
        <a href="peach.fuzzy.norms-module.html#PROB_INFERENCE" class="summary-name">PROB_INFERENCE</a> = <code title="ProbabilisticImplication, ProbabilisticAglutination">ProbabilisticImplication, ProbabilisticAgluti<code class="variable-ellipsis">...</code></code><br />
      Tuple containing, in order, probabilistic implication and algutination
    </td>
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        <a name="__package__"></a><span class="summary-name">__package__</span> = <code title="'peach.fuzzy'"><code class="variable-quote">'</code><code class="variable-string">peach.fuzzy</code><code class="variable-quote">'</code></code>
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      </tr>
    </table>
  </td>
</tr>
</table>
<a name="ZadehAnd"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ZadehAnd</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehAnd">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>And operation as defined by Lofti Zadeh.</p>
<p>And operation is the minimum of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ZadehOr"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ZadehOr</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehOr">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Or operation as defined by Lofti Zadeh.</p>
<p>Or operation is the maximum of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the or operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ZadehNot"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ZadehNot</span>(<span class="sig-arg">x</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehNot">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Not operation as defined by Lofti Zadeh.</p>
<p>Not operation is the complement to 1 of the given value, that is, <tt class="rst-docutils literal">1 - x</tt>.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the not operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ZadehImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ZadehImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ZadehImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Implication operation as defined by Zadeh.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the implication.</dd>
  </dl>
</td></tr></table>
</div>
<a name="DrasticProduct"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">DrasticProduct</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DrasticProduct">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Drastic product that can be used as and operation
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and operation</dd>
  </dl>
</td></tr></table>
</div>
<a name="DrasticSum"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">DrasticSum</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DrasticSum">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Drastic sum that can be used as or operation
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the or operation</dd>
  </dl>
</td></tr></table>
</div>
<a name="EinsteinProduct"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">EinsteinProduct</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#EinsteinProduct">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Einstein product that can be used as and operation.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="EinsteinSum"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">EinsteinSum</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#EinsteinSum">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Einstein sum that can be used as or operation.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the or operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="MamdaniImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">MamdaniImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#MamdaniImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Implication operation as defined by Mamdani.</p>
<p>Implication is the minimum of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the implication.</dd>
  </dl>
</td></tr></table>
</div>
<a name="MamdaniAglutination"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">MamdaniAglutination</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#MamdaniAglutination">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Aglutination as defined by Mamdani.</p>
<p>Aglutination is the maximum of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the aglutination.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ProbabilisticAnd"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ProbabilisticAnd</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticAnd">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>And operation as a probabilistic operation.</p>
<p>And operation is the product of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ProbabilisticOr"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ProbabilisticOr</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticOr">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Or operation as a probabilistic operation.</p>
<p>Or operation is given as the probability of the intersection of two events,
that is, x + y - xy.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the or operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ProbabilisticNot"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ProbabilisticNot</span>(<span class="sig-arg">x</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticNot">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Not operation as a probabilistic operation.</p>
<p>Not operation is the complement to 1 of the given value, that is, <tt class="rst-docutils literal">1 - x</tt>.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the not operation.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ProbabilisticImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ProbabilisticImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Implication as a probabilistic operation.</p>
<p>Implication is the product of the two values.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and implication.</dd>
  </dl>
</td></tr></table>
</div>
<a name="ProbabilisticAglutination"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">ProbabilisticAglutination</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#ProbabilisticAglutination">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Implication as a probabilistic operation.</p>
<p>Implication is given as the probability of the intersection of two events,
that is, x + y - xy.</p>
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the and algutination.</dd>
  </dl>
</td></tr></table>
</div>
<a name="DienesRescherImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">DienesRescherImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#DienesRescherImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Natural implication as in truth table, defined by Dienes-Rescher
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the implication.</dd>
  </dl>
</td></tr></table>
</div>
<a name="LukasiewiczImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">LukasiewiczImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#LukasiewiczImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Implication of the Lukasiewicz three-valued logic.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the implication.</dd>
  </dl>
</td></tr></table>
</div>
<a name="GodelImplication"></a>
<div>
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">GodelImplication</span>(<span class="sig-arg">x</span>,
        <span class="sig-arg">y</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="peach.fuzzy.norms-pysrc.html#GodelImplication">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  Implication as defined by Godel.
  <dl class="fields">
    <dt>Returns:</dt>
        <dd>The result of the implication.</dd>
  </dl>
</td></tr></table>
</div>
<br />
<!-- ==================== VARIABLES DETAILS ==================== -->
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  <td colspan="2" class="table-header">
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         class="privatelink" onclick="toggle_private();"
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  <h3 class="epydoc">__doc__</h3>
  
  <dl class="fields">
  </dl>
  <dl class="fields">
    <dt>Value:</dt>
      <dd><table><tr><td><pre class="variable">
&quot;&quot;&quot;
This package implements operations of fuzzy logic.

Basic operations are ``and (&amp;)``, ``or (|)`` and ``not (~)``. Those ar<span class="variable-linewrap"><img src="crarr.png" alt="\" /></span>
e
implemented as functions of, respectively, two, two and one values. Th<span class="variable-linewrap"><img src="crarr.png" alt="\" /></span>
e ``and``
is the t-norm of the fuzzy logic, and it is a function that takes two <span class="variable-linewrap"><img src="crarr.png" alt="\" /></span>
<code class="variable-ellipsis">...</code>
</pre></td></tr></table>
</dd>
  </dl>
</td></tr></table>
</div>
<a name="PROB_INFERENCE"></a>
<div>
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       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <h3 class="epydoc">PROB_INFERENCE</h3>
  Tuple containing, in order, probabilistic implication and algutination
  <dl class="fields">
  </dl>
  <dl class="fields">
    <dt>Value:</dt>
      <dd><table><tr><td><pre class="variable">
ProbabilisticImplication, ProbabilisticAglutination
</pre></td></tr></table>
</dd>
  </dl>
</td></tr></table>
</div>
<br />
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